A combined X-FEM and level set approach for modeling composite material's micro structure

Abstract

Composite materials are usually made of fibers and binding matrix. It’s always a challenge to model composite materials’ microstructure through the traditional finite element method because construction of an approximation space which is discontinuous across a given line or surface will place strict restrictions on the FE mesh. The interfacing of fibers in composites’ microstructure through the standard finite element method is irksome and tedious because the presence of fiber presents a discontinuity in the binding material. In this present work, the composite’s microstructure is modeled through the combined approach of Level Set and Extended Finite Element Method. The fiber is modeled implicitly through level set initialized by sign distance function within the framework of XFEM where mesh edges and faces do not have to align with discontinuities (e.g. cracks, holes, interfaces, etc). In XFEM, an enrichment function is used to locally enrich the approximation space by classical Finite Element Method that enables the precise approximation of discontinuity. Theoretical background information is provided on XFEM, Level Set Method, signed distance computation and its algorithms with the description of fiber modeling technique. ^